Continuous approaches to optimisation of composite laminates allow optimisation of a laminate's in-plane stiffness by optimising the laminate thickness, the percentages of plies oriented along different directions, and the directions of these plies. However, conventional methods do not optimise the laminate's stacking sequence (that is, the sequence of ply orientation angles through the stack) and simplistic assumptions are made about the laminates bending stiffness. This may, when converting the continuous design description into a discrete laminate stacking sequence, lead to significant changes in bending stiffness driven behaviours like buckling. Also additional weight could be added when rounding continuous laminate thickness and ply percentage data into a discrete ply solution, where to be conservative and to achieve a symmetric laminate, it may be required to increase the thickness associated with each discrete ply orientation to a value corresponding to an integer and even ply count. A symmetric laminate is a laminate with a stacking sequence that is symmetrical about its centre. For instance 0°, +45°, 90°, 90°, +45°, 0° is a symmetrical stacking sequence with an even ply count of six.
Composite laminate optimisation methods that allow the use of discrete stacking sequence information in the optimisation may be obtained using predefined stacking sequence tables. A stacking sequence table is used to define the laminate stacking sequence at discrete thickness values. Continuous sizing optimisation can then be performed using interpolation of properties between values found at discrete thicknesses and simple schemes can be devised to force sizing optimisation results to thickness values corresponding to integer ply counts. Stacking sequence tables used with such formulations are normally constructed such that through-thickness stacking sequence rules are satisfied and ply continuity rules are satisfied between discrete thickness values. Optimisation methods as such provide a sizing capability that uses stacking sequence data in the structural analysis and overcomes the previously described round-off problems. However, such methods do not permit optimisation of the laminate's stacking sequence, which is predefined by the stacking sequence table.
Continuous approaches to stacking sequence optimisation may be achieved by formulating the discrete stacking sequence optimisation problem in a continuous form, sub-dividing each ply into a number of sub-plies and optimising the thickness of sub-plies with a constraint on the total ply thickness. Such methods allow a gradual exchange of one sub-ply, having a specific orientation, for other sub-plies having different orientations. Such an approach is described, for example, in Stegmann J, Lund E (2005): “Discrete material optimization of general composite shell structures”. International Journal for Numerical Methods in Engineering, 62(14), pp. 2009-2027. A first disadvantage with this approach is that it formulates an optimisation problem with far too many design variables. A second disadvantage is that it does not achieve ply continuity between adjacent zones. That is, the fibre direction in each zone can take any value so adjacent zones may have fibre directions which vary by up to 90°.